This documentation is automatically generated by competitive-verifier/competitive-verifier
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1600
// competitive-verifier: TLE 2.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#include <tuple>
// Q=2*10^5 で 2*Q回クエリあるみたいなもんだけど 通る
#include "src/Math/ModInt.hpp"
#include "src/DataStructure/UnionFind.hpp"
#include "src/Graph/Graph.hpp"
#include "src/Graph/HeavyLightDecomposition.hpp"
#include "src/DataStructure/KDTree.hpp"
using namespace std;
struct RMQ {
using T= int;
static T ti() { return 0x7fffffff; }
static T op(T a, T b) { return min(a, b); }
};
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
using Mint= ModInt<1000000007>;
int N, M;
cin >> N >> M;
vector<Edge> es(M);
for (int i= 0; i < M; ++i) cin >> es[i], --es[i];
Graph g(N);
vector<Mint> C;
Mint w= 1;
UnionFind uf(N);
vector<char> used(M);
for (int i= 0; i < M; ++i) {
auto [A, B]= es[i];
w+= w;
if (uf.unite(A, B)) {
used[i]= true;
g.add_edge(A, B), C.push_back(w);
}
}
HeavyLightDecomposition tree(g);
auto adj= g.adjacency_edge(0);
vector<Mint> dep(N);
for (int i= 0, v; i < N; ++i)
for (int e: adj[v= tree.to_vertex(i)])
if (int u= g[e].to(v); u != tree.parent(v)) dep[u]= dep[v] + C[e];
auto dist= [&](int u, int v) { return dep[u] + dep[v] - dep[tree.lca(u, v)] * 2; };
vector<array<int, 3>> xyw;
for (int i= 0; i < M; ++i) {
if (used[i]) continue;
auto [A, B]= es[i];
int a= tree.to_seq(A), b= tree.to_seq(B);
if (a > b) swap(a, b);
xyw.push_back({a, b, i});
}
KDTree<int, 2, RMQ> kdt(xyw);
int Q;
cin >> Q;
while (Q--) {
int u, v, e;
cin >> u >> v >> e, --u, --v, --e;
auto [x, y]= es[e];
if (tree.parent(y) == x) swap(x, y);
bool u_in= tree.in_subtree(u, x);
if (!used[e] || u_in == tree.in_subtree(v, x)) {
cout << dist(u, v) << '\n';
continue;
}
auto [l, r]= tree.subtree(x);
int i= min(kdt.prod_cuboid(0, l - 1, l, r - 1), kdt.prod_cuboid(l, r - 1, r, N));
if (i > M) {
cout << -1 << '\n';
continue;
}
auto [p, q]= es[i];
if (!u_in) swap(u, v);
if (tree.in_subtree(q, x)) swap(p, q);
cout << dist(u, p) + dist(v, q) + Mint(2).pow(i + 1) << '\n';
}
return 0;
}
#line 1 "test/yukicoder/1600.KDT.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1600
// competitive-verifier: TLE 2.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#include <tuple>
// Q=2*10^5 で 2*Q回クエリあるみたいなもんだけど 通る
#line 2 "src/Math/mod_inv.hpp"
#include <utility>
#include <type_traits>
#include <cassert>
template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) {
std::make_signed_t<Uint> x= 1, y= 0, z= 0;
for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q;
return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
#line 2 "src/Internal/Remainder.hpp"
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
struct MP_Na { // mod < 2^32
u32 mod;
constexpr MP_Na(): mod(0) {}
constexpr MP_Na(u32 m): mod(m) {}
constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
constexpr inline u32 set(u32 n) const { return n; }
constexpr inline u32 get(u32 n) const { return n; }
constexpr inline u32 norm(u32 n) const { return n; }
constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo { // mod < 2^32, mod < 2^62
u_t mod;
constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
constexpr inline u_t set(u_t n) const { return mul(n, r2); }
constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
u_t iv, r2;
static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br { // 2^20 < mod <= 2^41
u64 mod;
constexpr MP_Br(): mod(0), x(0) {}
constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
static constexpr inline u64 set(u64 n) { return n; }
constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
u64 x;
constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 { // mod < 2^63, mod < 2^64
u64 mod;
constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
constexpr inline u64 set(u64 n) const { return n; }
constexpr inline u64 get(u64 n) const { return n; }
constexpr inline u64 norm(u64 n) const { return n; }
constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
u8 s;
u64 d, v;
constexpr inline u64 rem(const u128 &u) const {
u128 q= (u >> 64) * v + u;
u64 r= u64(u) - (q >> 64) * d - d;
if (r > u64(q)) r+= d;
if (r >= d) r-= d;
return r;
}
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) {
for (u_t ret= md.set(1);; x= md.mul(x, x))
if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
}
#line 3 "src/Internal/modint_traits.hpp"
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
#line 6 "src/Math/ModInt.hpp"
namespace math_internal {
template <class MP, u64 MOD> struct SB: s_b {
protected:
static constexpr MP md= MP(MOD);
};
template <class U, class B> struct MInt: public B {
using Uint= U;
static constexpr inline auto mod() { return B::md.mod; }
constexpr MInt(): x(0) {}
template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
constexpr MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
constexpr MInt name const { \
MInt ret; \
return ret.x= op, ret; \
}
FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); }
constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; }
constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; }
constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; }
constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; }
constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); }
constexpr bool operator!=(const MInt &r) const { return !(*this == r); }
constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); }
constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); }
constexpr inline Uint val() const { return B::md.get(x); }
friend ostream &operator<<(ostream &os, const MInt &r) { return os << r.val(); }
friend istream &operator>>(istream &is, MInt &r) {
i64 v;
return is >> v, r= MInt(v), is;
}
private:
Uint x;
};
template <u64 MOD> using MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>;
template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>;
}
using math_internal::ModInt;
#line 3 "src/DataStructure/UnionFind.hpp"
#include <algorithm>
class UnionFind {
std::vector<int> par;
public:
UnionFind(int n): par(n, -1) {}
int leader(int u) { return par[u] < 0 ? u : par[u]= leader(par[u]); }
bool unite(int u, int v) {
if ((u= leader(u)) == (v= leader(v))) return false;
if (par[u] > par[v]) std::swap(u, v);
return par[u]+= par[v], par[v]= u, true;
}
bool connected(int u, int v) { return leader(u) == leader(v); }
int size(int u) { return -par[leader(u)]; }
};
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#line 6 "src/Internal/ListRange.hpp"
#define _LR(name, IT, CT) \
template <class T> struct name { \
using Iterator= typename std::vector<T>::IT; \
Iterator bg, ed; \
Iterator begin() const { return bg; } \
Iterator end() const { return ed; } \
size_t size() const { return std::distance(bg, ed); } \
CT &operator[](int i) const { return bg[i]; } \
}
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
std::vector<T> dat;
std::vector<int> p;
size_t size() const { return p.size() - 1; }
ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
os << '[';
for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
using std::pair<int, int>::pair;
Edge &operator--() { return --first, --second, *this; }
int to(int v) const { return first ^ second ^ v; }
friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
size_t n;
Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
size_t vertex_size() const { return n; }
size_t edge_size() const { return size(); }
size_t add_vertex() { return n++; }
size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
for (auto [u, v]: *this) a; \
for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
for (int i= size(); i--;) { \
auto [u, v]= (*this)[i]; \
b; \
}
#define _ADJ(a, b) \
vector<int> p(n + 1), c(size() << !dir); \
if (!dir) { \
_ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
} else if (dir > 0) { \
_ADJ_FOR(++p[u], c[--p[u]]= a) \
} else { \
_ADJ_FOR(++p[v], c[--p[v]]= b) \
} \
return {c, p}
CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 5 "src/Graph/HeavyLightDecomposition.hpp"
class HeavyLightDecomposition {
std::vector<int> P, PP, D, I, L, R;
public:
HeavyLightDecomposition()= default;
HeavyLightDecomposition(const Graph &g, int root= 0): HeavyLightDecomposition(g.adjacency_vertex(0), root) {}
HeavyLightDecomposition(const CSRArray<int> &adj, int root= 0) {
const int n= adj.size();
P.assign(n, -2), PP.resize(n), D.resize(n), I.resize(n), L.resize(n), R.resize(n);
auto f= [&, i= 0, v= 0, t= 0](int r) mutable {
for (P[r]= -1, I[t++]= r; i < t; ++i)
for (int u: adj[v= I[i]])
if (P[v] != u) P[I[t++]= u]= v;
};
f(root);
for (int r= 0; r < n; ++r)
if (P[r] == -2) f(r);
std::vector<int> Z(n, 1), nx(n, -1);
for (int i= n, v; i--;) {
if (P[v= I[i]] == -1) continue;
if (Z[P[v]]+= Z[v]; nx[P[v]] == -1) nx[P[v]]= v;
if (Z[nx[P[v]]] < Z[v]) nx[P[v]]= v;
}
for (int v= n; v--;) PP[v]= v;
for (int v: I)
if (nx[v] != -1) PP[nx[v]]= v;
for (int v: I)
if (P[v] != -1) PP[v]= PP[PP[v]], D[v]= D[P[v]] + 1;
for (int i= n; i--;) L[I[i]]= i;
for (int v: I) {
int ir= R[v]= L[v] + Z[v];
for (int u: adj[v])
if (u != P[v] && u != nx[v]) L[u]= (ir-= Z[u]);
if (nx[v] != -1) L[nx[v]]= L[v] + 1;
}
for (int i= n; i--;) I[L[i]]= i;
}
int to_seq(int v) const { return L[v]; }
int to_vertex(int i) const { return I[i]; }
size_t size() const { return P.size(); }
int parent(int v) const { return P[v]; }
int head(int v) const { return PP[v]; }
int root(int v) const {
for (v= PP[v];; v= PP[P[v]])
if (P[v] == -1) return v;
}
bool connected(int u, int v) const { return root(u) == root(v); }
// u is in v
bool in_subtree(int u, int v) const { return L[v] <= L[u] && L[u] < R[v]; }
int subtree_size(int v) const { return R[v] - L[v]; }
int lca(int u, int v) const {
for (;; v= P[PP[v]]) {
if (L[u] > L[v]) std::swap(u, v);
if (PP[u] == PP[v]) return u;
}
}
int la(int v, int k) const {
assert(k <= D[v]);
for (int u;; k-= L[v] - L[u] + 1, v= P[u])
if (L[v] - k >= L[u= PP[v]]) return I[L[v] - k];
}
int jump(int u, int v, int k) const {
if (!k) return u;
if (u == v) return -1;
if (k == 1) return in_subtree(v, u) ? la(v, D[v] - D[u] - 1) : P[u];
int w= lca(u, v), d_uw= D[u] - D[w], d_vw= D[v] - D[w];
return k > d_uw + d_vw ? -1 : k <= d_uw ? la(u, k) : la(v, d_uw + d_vw - k);
}
int depth(int v) const { return D[v]; }
int dist(int u, int v) const { return D[u] + D[v] - D[lca(u, v)] * 2; }
// half-open interval [l,r)
std::pair<int, int> subtree(int v) const { return {L[v], R[v]}; }
// sequence of closed intervals [l,r]
std::vector<std::pair<int, int>> path(int u, int v, bool edge= 0) const {
std::vector<std::pair<int, int>> up, down;
while (PP[u] != PP[v]) {
if (L[u] < L[v]) down.emplace_back(L[PP[v]], L[v]), v= P[PP[v]];
else up.emplace_back(L[u], L[PP[u]]), u= P[PP[u]];
}
if (L[u] < L[v]) down.emplace_back(L[u] + edge, L[v]);
else if (L[v] + edge <= L[u]) up.emplace_back(L[u], L[v] + edge);
return up.insert(up.end(), down.rbegin(), down.rend()), up;
}
};
#line 4 "src/DataStructure/KDTree.hpp"
#include <numeric>
#include <map>
#include <set>
#line 8 "src/DataStructure/KDTree.hpp"
#include <cstdint>
#line 3 "src/Internal/HAS_CHECK.hpp"
#define MEMBER_MACRO(member, Dummy, name, type1, type2, last) \
template <class tClass> struct name##member { \
template <class U, Dummy> static type1 check(U *); \
static type2 check(...); \
static tClass *mClass; \
last; \
}
#define HAS_CHECK(member, Dummy) MEMBER_MACRO(member, Dummy, has_, std::true_type, std::false_type, static const bool value= decltype(check(mClass))::value)
#define HAS_MEMBER(member) HAS_CHECK(member, int dummy= (&U::member, 0))
#define HAS_TYPE(member) HAS_CHECK(member, class dummy= typename U::member)
#define HOGE_OR(member, name, type2) \
MEMBER_MACRO(member, class dummy= typename U::member, name, typename U::member, type2, using type= decltype(check(mClass))); \
template <class tClass> using name##member##_t= typename name##member<tClass>::type
#define NULLPTR_OR(member) HOGE_OR(member, nullptr_or_, std::nullptr_t)
#define MYSELF_OR(member) HOGE_OR(member, myself_or_, tClass)
#line 5 "src/Internal/tuple_traits.hpp"
#include <cstddef>
template <class T> static constexpr bool tuple_like_v= false;
template <class... Args> static constexpr bool tuple_like_v<std::tuple<Args...>> = true;
template <class T, class U> static constexpr bool tuple_like_v<std::pair<T, U>> = true;
template <class T, size_t K> static constexpr bool tuple_like_v<std::array<T, K>> = true;
template <class T> auto to_tuple(const T &t) {
if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::make_tuple(x...); }, t);
}
template <class T> auto forward_tuple(const T &t) {
if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::forward_as_tuple(x...); }, t);
}
template <class T> static constexpr bool array_like_v= false;
template <class T, size_t K> static constexpr bool array_like_v<std::array<T, K>> = true;
template <class T, class U> static constexpr bool array_like_v<std::pair<T, U>> = std::is_convertible_v<T, U>;
template <class T> static constexpr bool array_like_v<std::tuple<T>> = true;
template <class T, class U, class... Args> static constexpr bool array_like_v<std::tuple<T, U, Args...>> = array_like_v<std::tuple<T, Args...>> && std::is_convertible_v<U, T>;
template <class T> auto to_array(const T &t) {
if constexpr (array_like_v<T>) return std::apply([](auto &&...x) { return std::array{x...}; }, t);
}
template <class T> using to_tuple_t= decltype(to_tuple(T()));
template <class T> using to_array_t= decltype(to_array(T()));
#line 2 "src/Internal/long_traits.hpp"
// clang-format off
template<class T>struct make_long{using type= T;};
template<>struct make_long<char>{using type= short;};
template<>struct make_long<unsigned char>{using type= unsigned short;};
template<>struct make_long<short>{using type= int;};
template<>struct make_long<unsigned short>{using type= unsigned;};
template<>struct make_long<int>{using type= long long;};
template<>struct make_long<unsigned>{using type= unsigned long long;};
template<>struct make_long<long long>{using type= __int128_t;};
template<>struct make_long<unsigned long long>{using type= __uint128_t;};
template<>struct make_long<float>{using type= double;};
template<>struct make_long<double>{using type= long double;};
template<class T> using make_long_t= typename make_long<T>::type;
// clang-format on
#line 12 "src/DataStructure/KDTree.hpp"
namespace kdtree_internal {
template <class pos_t, size_t K, class M, class A, class B> class KDTreeImpl {};
template <class pos_t, size_t K, class M, class... PK, class... PK2> class KDTreeImpl<pos_t, K, M, std::tuple<PK...>, std::tuple<PK2...>> {
HAS_MEMBER(op);
HAS_MEMBER(ti);
HAS_MEMBER(mp);
HAS_MEMBER(cp);
HAS_TYPE(T);
HAS_TYPE(E);
MYSELF_OR(T);
NULLPTR_OR(E);
using Sec= std::array<pos_t, 2>;
using Pos= std::array<pos_t, K>;
using Range= std::array<Sec, K>;
using long_pos_t= make_long_t<pos_t>;
template <class L> static constexpr bool monoid_v= std::conjunction_v<has_T<L>, has_op<L>, has_ti<L>>;
template <class L> static constexpr bool dual_v= std::conjunction_v<has_T<L>, has_E<L>, has_mp<L>, has_cp<L>>;
struct Node_BB {
int ch[2]= {-1, -1};
Pos pos;
pos_t range[K][2];
};
template <class U> struct Node_B: Node_BB {
U val;
};
template <class D, bool sg, bool du> struct Node_D: Node_B<M> {};
template <bool sg, bool du> struct Node_D<void, sg, du>: Node_BB {};
template <class D> struct Node_D<D, 1, 0>: Node_B<typename M::T> {
typename M::T sum;
};
template <class D> struct Node_D<D, 0, 1>: Node_B<typename M::T> {
typename M::E laz;
bool flg= false;
};
template <class D> struct Node_D<D, 1, 1>: Node_B<typename M::T> {
typename M::T sum;
typename M::E laz;
bool flg= false;
};
using Node= Node_D<M, monoid_v<M>, dual_v<M>>;
using Iter= typename std::vector<int>::iterator;
using T= std::conditional_t<std::is_void_v<M>, std::nullptr_t, myself_or_T_t<M>>;
using E= nullptr_or_E_t<M>;
template <class P> using canbe_Pos= std::is_convertible<to_tuple_t<P>, std::tuple<PK...>>;
template <class P> using canbe_PosV= std::is_convertible<to_tuple_t<P>, std::tuple<PK..., T>>;
template <class P, class U> static constexpr bool canbe_Pos_and_T_v= std::conjunction_v<canbe_Pos<P>, std::is_convertible<U, T>>;
std::vector<Node> ns;
static inline T def_val() {
if constexpr (monoid_v<M>) return M::ti();
else return T();
}
template <bool z, size_t k, class P> static inline auto get_(const P &p) {
if constexpr (z) return std::get<k>(p);
else return std::get<k>(p.first);
}
template <class P, size_t... I> Range to_range(const P &p, std::index_sequence<I...>) { return {(assert(std::get<I + I>(p) <= std::get<I + I + 1>(p)), Sec{std::get<I + I>(p), std::get<I + I + 1>(p)})...}; }
inline void update(int t) {
ns[t].sum= ns[t].val;
if (ns[t].ch[0] != -1) ns[t].sum= M::op(ns[t].sum, ns[ns[t].ch[0]].sum);
if (ns[t].ch[1] != -1) ns[t].sum= M::op(ns[t].sum, ns[ns[t].ch[1]].sum);
}
inline void propagate(int t, const E &x) {
if (t == -1) return;
if (ns[t].flg) M::cp(ns[t].laz, x);
else ns[t].laz= x, ns[t].flg= true;
M::mp(ns[t].val, x);
if constexpr (monoid_v<M>) M::mp(ns[t].sum, x);
}
inline void push(int t) {
if (ns[t].flg) ns[t].flg= false, propagate(ns[t].ch[0], ns[t].laz), propagate(ns[t].ch[1], ns[t].laz);
}
template <bool z, class P, size_t k> inline void set_range(int t, int m, Iter bg, Iter ed, const P *p) {
auto [mn, mx]= std::minmax_element(bg, ed, [&](int a, int b) { return get_<z, k>(p[a]) < get_<z, k>(p[b]); });
ns[t].range[k][0]= get_<z, k>(p[*mn]), ns[t].range[k][1]= get_<z, k>(p[*mx]), ns[t].pos[k]= get_<z, k>(p[m]);
}
template <bool z, class P, size_t... I> inline void set_range_lp(int t, int m, Iter bg, Iter ed, const P *p, std::index_sequence<I...>) { (void)(int[]){(set_range<z, P, I>(t, m, bg, ed, p), 0)...}; }
template <bool z, uint8_t div, class P> inline int build(int &ts, Iter bg, Iter ed, const P *p, const T &v= def_val()) {
if (bg == ed) return -1;
auto md= bg + (ed - bg) / 2;
int t= ts++;
std::nth_element(bg, md, ed, [&](int a, int b) { return get_<z, div>(p[a]) < get_<z, div>(p[b]); }), set_range_lp<z>(t, *md, bg, ed, p, std::make_index_sequence<K>());
if constexpr (z) {
if constexpr (!std::is_void_v<M>) {
if constexpr (std::tuple_size_v<P> == K + 1) ns[t].val= std::get<K>(p[*md]);
else ns[t].val= v;
}
} else ns[t].val= p[*md].second;
static constexpr uint8_t nx= div + 1 == K ? 0 : div + 1;
ns[t].ch[0]= build<z, nx>(ts, bg, md, p, v), ns[t].ch[1]= build<z, nx>(ts, md + 1, ed, p, v);
if constexpr (monoid_v<M>) update(t);
return t;
}
template <bool z, uint8_t div, class P> inline int build(Iter bg, Iter ed, const P *p, int &ts) {
if (bg == ed) return -1;
auto md= bg + (ed - bg) / 2;
int t= ts++;
std::nth_element(bg, md, ed, [&](int a, int b) { return get_<z, div>(p[a]) < get_<z, div>(p[b]); }), set_range_lp<z>(t, bg, ed, p, std::make_index_sequence<K>());
if constexpr (z) {
if constexpr (!std::is_void_v<M>) {
if constexpr (std::tuple_size_v<P> == K + 1) ns[t].val= std::get<K>(p[t]);
else ns[t].val= def_val();
}
} else ns[t].val= p[t].second;
static constexpr uint8_t nx= div + 1 == K ? 0 : div + 1;
ns[t].ch[0]= build<z, nx>(bg, md, p, ts), ns[t].ch[1]= build<z, nx>(md + 1, ed, p, ts);
if constexpr (monoid_v<M>) update(t);
return t;
}
static inline auto in_cuboid(const Range &r) {
return [r](const Pos &pos) {
for (uint8_t k= K; k--;)
if (r[k][1] < pos[k] || pos[k] < r[k][0]) return false;
return true;
};
}
static inline auto out_cuboid(const Range &r) {
return [r](const pos_t rr[K][2]) {
for (uint8_t k= K; k--;)
if (rr[k][1] < r[k][0] || r[k][1] < rr[k][0]) return true;
return false;
};
}
static inline auto inall_cuboid(const Range &r) {
return [r](const pos_t rr[K][2]) {
for (uint8_t k= K; k--;)
if (rr[k][0] < r[k][0] || r[k][1] < rr[k][1]) return false;
return true;
};
}
static inline long_pos_t min_dist2(const pos_t r[K][2], const Pos &pos) {
long_pos_t d2= 0, dx;
for (uint8_t k= K; k--;) dx= std::clamp(pos[k], r[k][0], r[k][1]) - pos[k], d2+= dx * dx;
return d2;
}
static inline auto in_ball(const Pos &c, long_pos_t r2) {
return [c, r2](const Pos &pos) {
long_pos_t d2= 0, dx;
for (uint8_t k= K; k--;) dx= pos[k] - c[k], d2+= dx * dx;
return d2 <= r2;
};
}
static inline auto inall_ball(const Pos &c, long_pos_t r2) {
return [c, r2](const pos_t rr[K][2]) {
long_pos_t d2= 0, dx0, dx1;
for (uint8_t k= K; k--;) dx0= rr[k][0] - c[k], dx1= rr[k][1] - c[k], d2+= std::max(dx0 * dx0, dx1 * dx1);
return d2 <= r2;
};
}
static inline auto out_ball(const Pos &c, long_pos_t r2) {
return [c, r2](const pos_t r[K][2]) { return min_dist2(r, c) > r2; };
}
inline void nns(int t, const Pos &pos, std::pair<int, long_pos_t> &ret) const {
if (t == -1) return;
long_pos_t d2= min_dist2(ns[t].range, pos);
if (ret.first != -1 && d2 >= ret.second) return;
long_pos_t dx= d2= 0;
for (uint8_t k= K; k--;) dx= pos[k] - ns[t].pos[k], d2+= dx * dx;
if (ret.first == -1 || d2 < ret.second) ret= {t, d2};
bool f= 0;
if (auto [l, r]= ns[t].ch; l != -1 && r != -1) f= min_dist2(ns[l].range, pos) > min_dist2(ns[r].range, pos);
nns(ns[t].ch[f], pos, ret), nns(ns[t].ch[!f], pos, ret);
}
template <class In, class Out> inline void col(int t, const In &in, const Out &out, std::vector<T> &ret) const {
if (t == -1 || out(ns[t].range)) return;
if (in(ns[t].pos)) ret.push_back(ns[t].val);
col(ns[t].ch[0], in, out, ret), col(ns[t].ch[1], in, out, ret);
}
template <class In, class InAll, class Out> inline T fld(int t, const In &in, const InAll &inall, const Out &out) {
if (t == -1 || out(ns[t].range)) return def_val();
if (inall(ns[t].range)) return ns[t].sum;
if constexpr (dual_v<M>) push(t);
T ret= M::op(fld(ns[t].ch[0], in, inall, out), fld(ns[t].ch[1], in, inall, out));
return in(ns[t].pos) ? M::op(ret, ns[t].val) : ret;
}
template <class In, class InAll, class Out> inline void app(int t, const In &in, const InAll &inall, const Out &out, const E &x) {
if (t == -1 || out(ns[t].range)) return;
if (inall(ns[t].range)) return propagate(t, x);
if (push(t); in(ns[t].pos)) M::mp(ns[t].val, x);
app(ns[t].ch[0], in, inall, out, x), app(ns[t].ch[1], in, inall, out, x);
if constexpr (monoid_v<M>) update(t);
}
template <bool z> inline bool set(int t, const Pos &pos, const T &x) {
if (t == -1) return false;
bool isok= true;
for (uint8_t k= K; k--; isok&= pos[k] == ns[t].pos[k])
if (ns[t].range[k][1] < pos[k] || pos[k] < ns[t].range[k][0]) return false;
if constexpr (dual_v<M>) push(t);
if (isok) {
if constexpr (z) ns[t].val= x;
else ns[t].val= M::op(ns[t].val, x);
} else if (!(isok= set<z>(ns[t].ch[0], pos, x))) isok= set<z>(ns[t].ch[1], pos, x);
if constexpr (monoid_v<M>)
if (isok) update(t);
return isok;
}
inline std::pair<T, bool> get(int t, const Pos &pos) {
if (t == -1) return {T(), false};
bool myself= true;
for (uint8_t k= K; k--; myself&= pos[k] == ns[t].pos[k])
if (ns[t].range[k][1] < pos[k] || pos[k] < ns[t].range[k][0]) return {T(), false};
if (myself) return {ns[t].val, true};
if constexpr (dual_v<M>) push(t);
auto ret= get(ns[t].ch[0], pos);
return !ret.second ? get(ns[t].ch[1], pos) : ret;
}
public:
template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> KDTreeImpl(const P *p, size_t n): ns(n) {
std::vector<int> ids(n);
int ts= 0;
std::iota(ids.begin(), ids.end(), 0), build<1, 0>(ts, ids.begin(), ids.end(), p);
}
template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> KDTreeImpl(const std::vector<P> &p): KDTreeImpl(p.data(), p.size()) {}
template <class P, typename= std::enable_if_t<canbe_Pos<P>::value>> KDTreeImpl(const std::set<P> &p): KDTreeImpl(std::vector(p.begin(), p.end())) {}
template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const P *p, size_t n, U v): ns(n) {
std::vector<int> ids(n);
int ts= 0;
std::iota(ids.begin(), ids.end(), 0), build<1, 0>(ts, ids.begin(), ids.end(), p, v);
}
template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::vector<P> &p, U v): KDTreeImpl(p.data(), p.size(), v) {}
template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::set<P> &p, U v): KDTreeImpl(std::vector(p.begin(), p.end()), v) {}
template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::pair<P, U> *p, size_t n): ns(n) {
std::vector<int> ids(n);
int ts= 0;
std::iota(ids.begin(), ids.end(), 0), build<0, 0>(ts, ids.begin(), ids.end(), p);
}
template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::vector<std::pair<P, U>> &p): KDTreeImpl(p.data(), p.size()) {}
template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::map<P, U> &p): KDTreeImpl(std::vector(p.begin(), p.end())) {}
std::vector<T> enum_cuboid(PK2... xs) {
static_assert(!std::is_void_v<M>, "\"enum_cuboid\" is not available");
std::vector<T> ret;
auto r= to_range(std::forward_as_tuple(xs...), std::make_index_sequence<K>());
return col(-ns.empty(), in_cuboid(r), out_cuboid(r), ret), ret;
}
std::vector<T> enum_ball(PK... xs, pos_t r) const {
static_assert(!std::is_void_v<M>, "\"enum_ball\" is not available");
std::vector<T> ret;
long_pos_t r2= long_pos_t(r) * r;
return col(-ns.empty(), in_ball({xs...}, r2), out_ball({xs...}, r2), ret), ret;
}
T prod_cuboid(PK2... xs) {
static_assert(monoid_v<M>, "\"prod_cuboid\" is not available");
auto r= to_range(std::forward_as_tuple(xs...), std::make_index_sequence<K>());
return fld(-ns.empty(), in_cuboid(r), inall_cuboid(r), out_cuboid(r));
}
T prod_ball(PK... xs, pos_t r) {
static_assert(monoid_v<M>, "\"prod_ball\" is not available");
long_pos_t r2= long_pos_t(r) * r;
return fld(-ns.empty(), in_ball({xs...}, r2), inall_ball({xs...}, r2), out_ball({xs...}, r2));
}
void apply_cuboid(PK2... xs, E a) {
static_assert(dual_v<M>, "\"apply_cuboid\" is not available");
auto r= to_range(std::forward_as_tuple(xs...), std::make_index_sequence<K>());
app(-ns.empty(), in_cuboid(r), inall_cuboid(r), out_cuboid(r), a);
}
void apply_ball(PK... xs, pos_t r, E a) {
static_assert(dual_v<M>, "\"apply_ball\" is not available");
long_pos_t r2= long_pos_t(r) * r;
app(-ns.empty(), in_ball({xs...}, r2), inall_ball({xs...}, r2), out({xs...}, r2), a);
}
void set(PK... xs, T v) { assert(ns.size()), assert(set<1>(0, {xs...}, v)); }
void mul(PK... xs, T v) {
static_assert(monoid_v<M>, "\"mul\" is not available");
assert(ns.size()), assert(set<0>(0, {xs...}, v));
}
T get(PK... xs) {
assert(ns.size());
auto [ret, flg]= get(0, {xs...});
return assert(flg), ret;
}
Pos nearest_neighbor(PK... xs) const {
assert(ns.size());
std::pair<int, long_pos_t> ret= {-1, -1};
return nns(0, {xs...}, ret), ns[ret.first].pos;
}
};
template <class pos_t, size_t K, class M= void> using KDTree= KDTreeImpl<pos_t, K, M, to_tuple_t<std::array<pos_t, K>>, to_tuple_t<std::array<pos_t, K + K>>>;
}
using kdtree_internal::KDTree;
#line 15 "test/yukicoder/1600.KDT.test.cpp"
using namespace std;
struct RMQ {
using T= int;
static T ti() { return 0x7fffffff; }
static T op(T a, T b) { return min(a, b); }
};
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
using Mint= ModInt<1000000007>;
int N, M;
cin >> N >> M;
vector<Edge> es(M);
for (int i= 0; i < M; ++i) cin >> es[i], --es[i];
Graph g(N);
vector<Mint> C;
Mint w= 1;
UnionFind uf(N);
vector<char> used(M);
for (int i= 0; i < M; ++i) {
auto [A, B]= es[i];
w+= w;
if (uf.unite(A, B)) {
used[i]= true;
g.add_edge(A, B), C.push_back(w);
}
}
HeavyLightDecomposition tree(g);
auto adj= g.adjacency_edge(0);
vector<Mint> dep(N);
for (int i= 0, v; i < N; ++i)
for (int e: adj[v= tree.to_vertex(i)])
if (int u= g[e].to(v); u != tree.parent(v)) dep[u]= dep[v] + C[e];
auto dist= [&](int u, int v) { return dep[u] + dep[v] - dep[tree.lca(u, v)] * 2; };
vector<array<int, 3>> xyw;
for (int i= 0; i < M; ++i) {
if (used[i]) continue;
auto [A, B]= es[i];
int a= tree.to_seq(A), b= tree.to_seq(B);
if (a > b) swap(a, b);
xyw.push_back({a, b, i});
}
KDTree<int, 2, RMQ> kdt(xyw);
int Q;
cin >> Q;
while (Q--) {
int u, v, e;
cin >> u >> v >> e, --u, --v, --e;
auto [x, y]= es[e];
if (tree.parent(y) == x) swap(x, y);
bool u_in= tree.in_subtree(u, x);
if (!used[e] || u_in == tree.in_subtree(v, x)) {
cout << dist(u, v) << '\n';
continue;
}
auto [l, r]= tree.subtree(x);
int i= min(kdt.prod_cuboid(0, l - 1, l, r - 1), kdt.prod_cuboid(l, r - 1, r, N));
if (i > M) {
cout << -1 << '\n';
continue;
}
auto [p, q]= es[i];
if (!u_in) swap(u, v);
if (tree.in_subtree(q, x)) swap(p, q);
cout << dist(u, p) + dist(v, q) + Mint(2).pow(i + 1) << '\n';
}
return 0;
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++-13 | in01.txt |
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5 ms | 3 MB |
g++-13 | in02.txt |
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5 ms | 4 MB |
g++-13 | in03.txt |
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4 ms | 4 MB |
g++-13 | in04.txt |
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4 ms | 4 MB |
g++-13 | in05.txt |
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131 ms | 18 MB |
g++-13 | in06.txt |
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134 ms | 18 MB |
g++-13 | in07.txt |
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6 ms | 4 MB |
g++-13 | in08.txt |
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5 ms | 4 MB |
g++-13 | in09.txt |
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5 ms | 3 MB |
g++-13 | in10.txt |
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5 ms | 3 MB |
g++-13 | in11.txt |
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140 ms | 16 MB |
g++-13 | in12.txt |
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155 ms | 16 MB |
g++-13 | in13.txt |
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165 ms | 18 MB |
g++-13 | in14.txt |
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150 ms | 17 MB |
g++-13 | in15.txt |
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134 ms | 18 MB |
g++-13 | in16.txt |
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6 ms | 4 MB |
g++-13 | in17.txt |
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5 ms | 4 MB |
g++-13 | in18.txt |
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153 ms | 17 MB |
g++-13 | in19.txt |
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133 ms | 18 MB |
g++-13 | in20.txt |
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6 ms | 4 MB |
g++-13 | in21.txt |
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5 ms | 4 MB |
g++-13 | in22.txt |
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155 ms | 17 MB |
g++-13 | in23.txt |
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6 ms | 4 MB |
g++-13 | in24.txt |
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5 ms | 4 MB |
g++-13 | in25.txt |
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136 ms | 18 MB |
g++-13 | in26.txt |
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6 ms | 4 MB |
g++-13 | in27.txt |
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5 ms | 3 MB |
g++-13 | in28.txt |
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5 ms | 4 MB |
g++-13 | in29.txt |
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5 ms | 3 MB |
g++-13 | in30.txt |
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632 ms | 17 MB |
g++-13 | in31.txt |
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791 ms | 17 MB |
g++-13 | in32.txt |
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162 ms | 17 MB |
g++-13 | in33.txt |
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134 ms | 17 MB |
g++-13 | in34.txt |
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6 ms | 4 MB |
g++-13 | in35.txt |
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5 ms | 4 MB |
g++-13 | in36.txt |
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120 ms | 18 MB |
g++-13 | in37.txt |
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88 ms | 18 MB |
g++-13 | in38.txt |
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6 ms | 4 MB |
g++-13 | in39.txt |
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166 ms | 17 MB |
g++-13 | in40.txt |
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6 ms | 3 MB |
g++-13 | in41.txt |
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795 ms | 17 MB |
g++-13 | in42.txt |
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315 ms | 17 MB |
g++-13 | in43.txt |
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361 ms | 17 MB |
g++-13 | in44.txt |
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361 ms | 17 MB |
g++-13 | in45.txt |
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437 ms | 17 MB |
g++-13 | in46.txt |
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744 ms | 17 MB |
g++-13 | in47.txt |
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110 ms | 17 MB |
g++-13 | in48.txt |
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1325 ms | 17 MB |
g++-13 | in49.txt |
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119 ms | 17 MB |
g++-13 | in50.txt |
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5 ms | 3 MB |
g++-13 | in51.txt |
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5 ms | 4 MB |
g++-13 | sample_01.txt |
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4 ms | 4 MB |
g++-13 | sample_02.txt |
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4 ms | 4 MB |
g++-13 | sample_03.txt |
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4 ms | 4 MB |
clang++-18 | in01.txt |
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5 ms | 4 MB |
clang++-18 | in02.txt |
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5 ms | 4 MB |
clang++-18 | in03.txt |
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4 ms | 4 MB |
clang++-18 | in04.txt |
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4 ms | 4 MB |
clang++-18 | in05.txt |
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162 ms | 18 MB |
clang++-18 | in06.txt |
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164 ms | 18 MB |
clang++-18 | in07.txt |
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5 ms | 4 MB |
clang++-18 | in08.txt |
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5 ms | 4 MB |
clang++-18 | in09.txt |
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5 ms | 4 MB |
clang++-18 | in10.txt |
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4 ms | 4 MB |
clang++-18 | in11.txt |
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135 ms | 17 MB |
clang++-18 | in12.txt |
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153 ms | 16 MB |
clang++-18 | in13.txt |
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184 ms | 17 MB |
clang++-18 | in14.txt |
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172 ms | 17 MB |
clang++-18 | in15.txt |
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159 ms | 18 MB |
clang++-18 | in16.txt |
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6 ms | 4 MB |
clang++-18 | in17.txt |
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5 ms | 4 MB |
clang++-18 | in18.txt |
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176 ms | 17 MB |
clang++-18 | in19.txt |
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161 ms | 18 MB |
clang++-18 | in20.txt |
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5 ms | 4 MB |
clang++-18 | in21.txt |
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7 ms | 4 MB |
clang++-18 | in22.txt |
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170 ms | 17 MB |
clang++-18 | in23.txt |
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5 ms | 4 MB |
clang++-18 | in24.txt |
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5 ms | 4 MB |
clang++-18 | in25.txt |
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158 ms | 18 MB |
clang++-18 | in26.txt |
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5 ms | 4 MB |
clang++-18 | in27.txt |
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5 ms | 4 MB |
clang++-18 | in28.txt |
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4 ms | 4 MB |
clang++-18 | in29.txt |
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4 ms | 4 MB |
clang++-18 | in30.txt |
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614 ms | 17 MB |
clang++-18 | in31.txt |
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781 ms | 17 MB |
clang++-18 | in32.txt |
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179 ms | 17 MB |
clang++-18 | in33.txt |
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150 ms | 17 MB |
clang++-18 | in34.txt |
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5 ms | 4 MB |
clang++-18 | in35.txt |
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4 ms | 4 MB |
clang++-18 | in36.txt |
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142 ms | 18 MB |
clang++-18 | in37.txt |
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94 ms | 18 MB |
clang++-18 | in38.txt |
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5 ms | 4 MB |
clang++-18 | in39.txt |
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170 ms | 17 MB |
clang++-18 | in40.txt |
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5 ms | 4 MB |
clang++-18 | in41.txt |
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773 ms | 17 MB |
clang++-18 | in42.txt |
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344 ms | 17 MB |
clang++-18 | in43.txt |
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405 ms | 17 MB |
clang++-18 | in44.txt |
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398 ms | 17 MB |
clang++-18 | in45.txt |
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463 ms | 18 MB |
clang++-18 | in46.txt |
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849 ms | 17 MB |
clang++-18 | in47.txt |
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114 ms | 17 MB |
clang++-18 | in48.txt |
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1474 ms | 17 MB |
clang++-18 | in49.txt |
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115 ms | 17 MB |
clang++-18 | in50.txt |
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5 ms | 4 MB |
clang++-18 | in51.txt |
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5 ms | 4 MB |
clang++-18 | sample_01.txt |
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4 ms | 4 MB |
clang++-18 | sample_02.txt |
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4 ms | 4 MB |
clang++-18 | sample_03.txt |
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4 ms | 4 MB |